Place the chicken, celery, carrots, and dill into a large stockpot. Add the water, and a little salt (you can add more later), and pepper to taste. Bring to a boil, cover and simmer for 1-1/2 to 2 hours.

Remove the chicken. If using the roaster, take the meat off the bones and place in a covered container. Skim out the vegetables and place in the container with the chicken. Add a little broth to keep the meat moist. Cover and refrigerate until ready to use.

Skim off as much fat as possible from the soup. If the soup lacks flavor, either add some powdered bouillon to taste, or simmer the soup down to concentrate the flavors.

Taste the soup and adjust the salt and pepper to taste (do not add more salt until before reducing it, or it will be too salty). When the soup has the flavor you like, it can be used immediately to make the matzo balls, or can be refrigerated overnight.

The next day, remove any fat that has solidified on the top of the soup (you can cook the matzo balls without refrigerating the stock, especially if you have done a good job of skimming off all fat, or if you are using canned stock).

If serving immediately, add back in the reserved vegetables and chicken (if using). Let heat through, and then serve.

If you don't like the way clear broth looks or feels in the mouth, finely chop some of the vegetables in the processor, and add them back to the broth.

Poster's Notes:
I love my soup to be cloudy! I grind up some carrots, too, as I don't like having the broth be so clear--to me that's unappetizing, plus the matzo balls taste so much better when they're cooked in the soup. Clearly, a matter of taste!